If you're really struggling, gear is the likely culprit. That can be both your own and the tank's.

If every time you look at the tank you're panicking at his HP level, try moving your party frame closer to the center of the screen. And lastly... yes, there's a very strong push for healers to DPS. But if you're struggling, don't, just focus on healing. At the end of the day a party can get by without healer DPS, they can't get by without healer heals.

Good luck out there.